This book systematically introduces the basic theories and methods of stock index futures, focusing on arbitrage trading and hedging trading of stock index futures. This book is divided into three parts. The first part includes 1 ~ 4 chapters, which mainly introduces the basic concepts of stock index futures, such as futures, forwards, stock indexes, stock index futures, trading strategies, pricing methods and risk control. The second part, including chapters 5-7, mainly introduces the concept and methods of arbitrage trading in stock index futures, focusing on the practical method of determining the arbitrage boundary and the key technology to realize arbitrage strategy-index replication method. The third part, including the eighth and ninth chapters, mainly introduces the hedging methods of using stock index futures to manage systemic risks, focusing on the optimal hedging methods of stock index futures, using different risk measures, such as VaRiance and var. Considering the transaction cost, the determination method of the optimal hedging ratio and the hedging efficiency. This book is suitable for researchers engaged in stock index futures, financial engineering and empirical analysis, as well as those engaged in financial risk control, management and financial derivative product development. It can also be used for the teaching of senior undergraduates, postgraduates and teachers majoring in financial engineering, financial mathematics, computational mathematics and applied mathematics.